Instantaneous frequency estimation at low signal-to-noise ratios using time-varying notch filters

• Published in: Signal processing Vol. 88; no. 5; pp. 1271 - 1288
• Main Authors: Johansson, A. Torbjörn, White, Paul R.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.05.2008; Elsevier Science
• Subjects: Applied sciences; Basis function; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Information, signal and communications theory; Instantaneous frequency estimation; Model order determination; Notch filter; Recursive prediction error estimation; Signal and communications theory; Signal, noise; Telecommunications and information theory; Time-varying AR model; Time-varying notch filter; AWGN; Time-varying AR model; RPE; LS; Instantaneous frequency estimation; Notch filter; Basis function; MDL; TVAR; Model order determination; SNR; RLS; Time-varying notch filter; AIC; ARMA; IF; TVNF; MSE; RPLR; AR; Recursive prediction error estimation; ANF; RMS; FPE; WGN; Parameter estimation; Error estimation; Signal estimation; Iterative method; Frequency estimation; Autoregressive model; Modeling; Adaptive method; Time variation; Parametric method; Instantaneous frequency; Additive noise; Design criterion; Adaptive filter; Search algorithm; Time-varying filters; Recursive estimation; Signal to noise ratio
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2007.11.014

This paper is aimed at finding parametric signal models that perform well at modelling noisy tonals at low signal-to-noise ratios (SNRs). We focus on models that are applied to a segment of data at a time, rather than work their way through the data in a sequential manner as typified by the adaptive methods. Inspired by notch filter theory, we extend the well-known time-varying AR (TVAR) models to include the effects of additive noise, and arrive at two types of time-varying notch filter (TVNF). The first one, like the TVAR model, employs a basis expansion of the filter coefficients. For the second one, we utilise the fact that tonal instantaneous frequencies (IFs) are directly proportional to the angles of the roots of the denominator polynomial, and perform a basis expansion of the IFs. Adaptive notch filters are well known and have been successfully applied in several fields. By application to simulated signals and a section of a dolphin whistle recording, it is shown that the TVNFs perform better than the TVAR model, and are useful tools for low SNR IF estimation. TVNF estimation employs a regularised Gauss–Newton type iterative search algorithm, which exhibits rapid and reliable convergence. Model order determination by Akaike's final prediction error (FPE) criterion is also discussed along with the selection of notch filter design and regularisation parameters.